Yeah that's the kind of hand waving problems away that I kind feared. I'm not sure you've got the perspective to really understand what some folks are dealing with in life if you can just so easily hand wave so many things.
I rather consider your kind of argument to be hand wavy. "Some people simply have no options or opportunities whatsoever". Can you provide some actual examples? And what is even the point to talk about those hypothetical people? Since nothing can be done, their situation can never ever change, there is no point in discussing it.
Yes there may be some people who are too sick to work. Everybody else can go look for another job. And the ones who are too sick to work probably have other people taking care of their kids already. So those other people can go look for another job.